Finite Group Databasebeta

← #72287296

Subgroups — #72287296

Order 1024.

2520 conjugacy classes of subgroups.

The subgroup lattice has 916 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#33669C211yesmaximal, characteristic
2#6344817C211yesmaximal, characteristic, complemented
3C2×#17895C211yesmaximal, characteristic, complemented
4#483934C218yesmaximal, complemented
5#483921C218yesmaximal, complemented
6#483843C214yesmaximal, complemented
7#483813C214yesmaximal, complemented
8#483420C211yesmaximal, characteristic, complemented
9#481315C211yesmaximal, characteristic, complemented
10#481279C211yesmaximal, characteristic, complemented
11#479969C211yesmaximal, characteristic, complemented
12C2×#3169C2211yescharacteristic
13#60236—21no—
14C2×#2975—21no—
15C22×C4×D8C2211yescharacteristic
16#33669C414yes—
17#33669C414yes—
18#33669C2214yes—
19#33669C2214yes—
20C2×#2233C412yes—
21C2×#2226C412yes—
22C2×#2206C412yes—
23C2×#2184C412yes—
24C2×#2177C2214yes—
25#33418C2211yescharacteristic
26C2×#2163C2211yescharacteristic
27#17970—22no—
28#17970C2214yescomplemented
29#17962C2214yescomplemented
30#17956—22no—
31#17895—21no—
32#17895—22no—
33#17895—21no—
34#17895—21no—
35#17895C2212yes—
36#17895C2212yes—
37#17895C2214yescomplemented
38#17895C2212yescomplemented
39C2×#1594C2214yescomplemented
40C2×#1589—22no—
41#17854—21no—
42#17854C2212yescomplemented
43#17793C2211yescharacteristic
44C2×#1564C2211yescharacteristic
45#17478—21no—
46C2×#1478—21no—
47C2×#1450C2211yescharacteristic
48#12089C22132yescomplemented
49#12078C22132yescomplemented
50#12031C2214yescomplemented
51#12030C2214yescomplemented
52#11999C2214yescomplemented
53#11667C2214yescomplemented
54#11663C2214yescomplemented
55#11654C2214yescomplemented
56#11652C2214yescomplemented
57#11599C2214yes—
58#11599C2214yescomplemented
59#11416C2214yescomplemented
60#11415C2214yescomplemented
61#11406C2212yescomplemented
62#11405C2212yescomplemented
63C23×D8C2×C411yescharacteristic
64C2×#532—21no—
65C22×C4×D4—21no—
66C22×D16C2×C414yes—
67#3169—21no—
68#3169—21no—
69#3169—21no—
70#3169—21no—
71#3169C2×C412yes—
72#3169C2×C412yes—
73#3169C2312yes—
74#3169C2312yes—
75C2×#500C2×C411yescharacteristic
76C2×#493C2×C411yescharacteristic
77C2×#486—21no—
78C2×#466—21no—
79C2×#466C2×C412yes—
80#2981—24no—
81#2979—42no—
82#2975—22no—
83#2975—22no—
84#2975—24no—
85#2975—22no—
86#2975—42no—
87#2975—42no—
88#2974—42no—
89#2972—22no—
90C2×C4×D8—21no—
91C2×C4×D8—21no—
92C2×C4×D8—21no—
93C2×C4×D8—21no—
94C2×C4×D8—21no—
95C2×C4×D8—21no—
96C2×C4×D8—21no—
97C2×C4×D8C2×C412yes—
98C2×C4×D8C2×C412yes—
99C2×C4×D8C2×C412yes—
100C2×C4×D8C2312yes—
101C2×C4×D8C2312yes—
102C2×C4×D8C2312yes—
103C2×C4×D8C2312yes—
104#2935—42no—
105#2931—24no—
106C2×#436—24no—
107C2×#436—42no—
108#2920—21no—
109C2×#431—21no—
110C2×#431D411yescharacteristic
111C2×#431D411yescharacteristic
112C22×#107C2×C411yescharacteristic
113C22×#102—21no—
114#2880—42no—
115C2×#407—42no—
116C22×C4×C8C2311yescharacteristic
117#2233C2×C418yes—
118#2233C2×C418yes—
119#2226C2×C418yes—
120#2226C2×C418yes—
121#2206C2×C418yes—
122#2206C2×C418yes—
123#2184C2×C418yes—
124#2184C2×C418yes—
125#2177C2×C4116yes—
126#2177C23116yes—
127#2163C2×C412yes—
128#2163C2×C412yes—
129#2163C2312yes—
130#2163C2312yes—
131#2163C2312yes—
132#2163C2312yes—
133#2162—21no—
134#2162—21no—
135C2×#367C2×C414yes—
136#2150—21no—
137C2×C4⋊C16C2×C412yes—
138C2×#357C2×C414yes—
139C2×#357C2×C414yes—
140#2112—21no—
141C2×C22⋊C16C2×C412yes—
142C4×M32C2312yes—
143C2×#346C2312yes—
144#1594—24no—
145#1594—24no—
146#1594—24no—
147#1594C2318yes—
148#1594C2318yes—
149#1594C2318yescomplemented
150#1589—24no—
151#1589—24no—
152#1589—24no—
153#1589—24no—
154#1589—24no—
155#1589—24no—
156#1580—24no—
157#1580C2318yescomplemented
158C8×D8—24no—
159C8×D8—24no—
160#1568—21no—
161#1568C2312yes—
162#1567—21no—
163#1566C2312yes—
164#1564—21no—
165#1564—21no—
166#1564—21no—
167#1564C2312yes—
168#1564C2312yes—
169#1564C2312yes—
170C2×#335—21no—
171C2×#334C2312yes—
172#1496—24no—
173#1492—24no—
174#1478—22no—
175#1478—22no—
176#1478—24no—
177#1478—22no—
178#1478—22no—
179C2×D4⋊C8—24no—
180#1450D412yes—
181#1450D411yescharacteristic
182#1450D411yescharacteristic
183#1450C2312yes—
184#1450C2311yescharacteristic
185#1450C2311yescharacteristic
186C2×#322C2312yes—
187C2×C82D412yes—
188#1368C23116yescomplemented
189#1333C23116yes—
190#1333C23116yescomplemented
191#1313C2318yescomplemented
192#1313C2318yescomplemented
193C22×#41—41no—
194C23×D4—21no—
195C24×C4—41no—
196C22×D8—21no—
197C22×D8—21no—
198C22×D8—21no—
199C22×D8—21no—
200C22×D8—44no—
201C22×D8C22×C412yes—
202C22×D8C22×C412yes—
203C22×D8C22×C412yes—
204C22×D8C22×C412yes—
205C2×#131—44no—
206C22×M16—44no—
207C23×C8C22×C411yescharacteristic
208C23×C8#4111yescharacteristic
209#532—22no—
210#532—22no—
211#532—22no—
212#532—22no—
213#532—41no—
214#532—41no—
215#532—41no—
216#532—41no—
217C2×C4⋊Q8—21no—
218C2×#127—21no—
219C2×#124—41no—
220C2×#121—22no—
221C2×#121—41no—
222C2×C4×D4—22no—
223C2×C4×D4—22no—
224C2×C4×D4—22no—
225C2×C4×D4—22no—
226C2×C4×D4—22no—
227C2×C4×D4—22no—
228C2×C4×D4—22no—
229C2×C4×D4—41no—
230C2×C4×D4—41no—
231C2×C4×D4—41no—
232C2×C4×D4—41no—
233C2×C4×D4—41no—
234C2×C4×D4—41no—
235C2×C4×D4—41no—
236C22×C4⋊C4—21no—
237C22×C22⋊C4—41no—
238C22×C42C2×D411yescharacteristic
239C2×D16—48no—
240C2×D16C22×C4116yes—
241C2×M32—22no—
242C22×C16C22×C414yes—
243#500—21no—
244#500—21no—
245#500C22×C412yes—
246#500C22×C412yes—
247#493—21no—
248#493—21no—
249#493C22×C412yes—
250#493C22×C412yes—
251#486—22no—
252#486—22no—
253#486—22no—
254#486—22no—
255#466—22no—
256#466—22no—
257#466—22no—
258#466—22no—
259#466—22no—
260#466—22no—
261#466C22×C414yes—
262#466C22×C414yes—
263C4×D8—22no—
264C4×D8—22no—
265C4×D8—22no—
266C4×D8—22no—
267C4×D8—22no—
268C4×D8—22no—
269C4×D8—22no—
270C4×D8—22no—
271C4×D8—22no—
272C4×D8—22no—
273C4×D8—22no—
274C4×D8—22no—
275C4×D8—22no—
276C4×D8—22no—
277C4×D8—22no—
278C4×D8—22no—
279C4×D8—22no—
280C4×D8—22no—
281C4×D8C22×C414yes—
282C4×D8C22×C414yes—
283C4×D8C22×C414yes—
284C4×D8C22×C414yes—
285C4×D8C2414yes—
286C4×D8C2414yes—
287#436—28no—
288#436—28no—
289#436—28no—
290#436—44no—
291#436—44no—
292#436—44no—
293#436—44no—
294#436—44no—
295#436—48no—
296#436—44no—
297#435—48no—
298C8×D4—28no—
299C8×D4—44no—
300C8×D4—44no—
301#432—22no—
302#432—41no—
303#431—21no—
304#431—21no—
305#431—21no—
306#431—21no—
307#431—22no—
308#431—22no—
309#431—22no—
310#431—41no—
311#431—41no—
312#431—41no—
313#431C2×D411yescharacteristic
314#431C2×D411yescharacteristic
315#431C2×D411yescharacteristic
316#431C2×D411yescharacteristic
317#431C2×D412yes—
318#431C2×D412yes—
319C2×#107—21no—
320C2×#107—21no—
321C2×#107—21no—
322C2×#107—21no—
323C2×#107C22×C412yes—
324C2×#107C22×C412yes—
325C2×#107C22×C412yes—
326C2×#107C22×C412yes—
327#423—22no—
328C2×C4⋊C8—21no—
329C2×C4⋊C8—21no—
330C2×C4⋊C8—22no—
331C2×#102—22no—
332C2×#102—22no—
333C2×#102—22no—
334C2×#102—22no—
335C2×#102—22no—
336C2×#102—22no—
337C2×#102—22no—
338C2×#102—22no—
339#408—48no—
340#408—44no—
341#407—44no—
342#407—44no—
343#407—48no—
344#407—44no—
345#407—41no—
346C2×C22⋊C8—21no—
347C2×C22⋊C8—21no—
348C2×C22⋊C8—44no—
349C2×C22⋊C8—44no—
350C2×C22⋊C8—41no—
351C4×M16—41no—
352C2×C4×C8—41no—
353C2×C4×C8C22×C411yescharacteristic
354C2×C4×C8C22×C411yescharacteristic
355C2×C4×C8C22×C411yescharacteristic
356C2×C4×C8C2×D412yes—
357C2×C4×C8C2×D412yes—
358C2×C4×C8C2×D411yescharacteristic
359C2×C4×C8C2×D411yescharacteristic
360C2×C4×C8C2×D411yescharacteristic
361C2×C4×C8#4111yescharacteristic
362C2×C4×C8#4111yescharacteristic
363C2×C4×C8#4111yescharacteristic
364C2×C4×C8C2411yescharacteristic
365C2×C4×C8C2411yescharacteristic
366C2×C4×C8C2411yescharacteristic
367#367C22×C4116yes—
368C4⋊C16—22no—
369C4⋊C16—22no—
370C4⋊C16C22×C414yes—
371C4⋊C16C22×C414yes—
372#357C22×C4116yes—
373#357C22×C4116yes—
374C22⋊C16—22no—
375C22⋊C16—22no—
376C22⋊C16C22×C414yes—
377C22⋊C16C22×C414yes—
378#346C22×C414yes—
379#346C2414yes—
380#346C2414yes—
381C4×C16—22no—
382#335—22no—
383#335—22no—
384#335—22no—
385#335—22no—
386#334—22no—
387#334—22no—
388#334C2414yes—
389#334C2414yes—
390D4⋊C8—28no—
391D4⋊C8—28no—
392D4⋊C8—28no—
393D4⋊C8—28no—
394#322C2×D412yes—
395#322C2×D412yes—
396#322C2412yes—
397#322C2412yes—
398C82C2×D412yes—
399C82C2×D412yes—
400C82C2×D412yes—
401C82C2×D412yes—
402C25—41no—
403C2×#41—42no—
404C2×#41—42no—
405C2×#41—42no—
406C2×#41—42no—
407C2×#41—164no—
408C22×Q8—41no—
409C22×D4—22no—
410C22×D4—22no—
411C22×D4—22no—
412C22×D4—22no—
413C22×D4—44no—
414C22×D4—44no—
415C22×D4—42no—
416C22×D4—41no—
417C22×D4—41no—
418C22×D4—41no—
419C22×D4—41no—
420C22×D4—41no—
421C23×C4—41no—
422C23×C4—42no—
423C23×C4—42no—
424C23×C4—42no—
425C23×C4—42no—
426C23×C4—42no—
427C23×C4—42no—
428C23×C4—42no—
429C23×C4—164no—
430C23×C4C4×D411yescharacteristic
431C23×C4AGL(1,ℤ/8)11yescharacteristic
432C23×C4AGL(1,ℤ/8)11yescharacteristic
433C2×D8—22no—
434C2×D8—22no—
435C2×D8—22no—
436C2×D8—22no—
437C2×D8—22no—
438C2×D8—22no—
439C2×D8—24no—
440C2×D8—24no—
441C2×D8—28no—
442C2×D8—44no—
443C2×D8—44no—
444C2×D8—44no—
445C2×D8—44no—
446C2×D8—44no—
447C2×D8—44no—
448C2×D8C23×C414yes—
449C2×D8C23×C414yes—
450#131—168no—
451C2×M16—48no—
452C2×M16—48no—
453C2×M16—48no—
454C2×M16—42no—
455C2×M16—168no—
456C22×C8—24no—
457C22×C8—22no—
458C22×C8—22no—
459C22×C8—42no—
460C22×C8—48no—
461C22×C8—42no—
462C22×C8C4×D411yescharacteristic
463C22×C8C4×D411yescharacteristic
464C22×C8C4×D411yescharacteristic
465C22×C8C4×D411yescharacteristic
466C22×C8C4×D411yescharacteristic
467C22×C8C4×D411yescharacteristic
468C22×C8C23×C411yescharacteristic
469C22×C8C23×C411yescharacteristic
470C22×C8C23×C411yescharacteristic
471C22×C8C2×#4111yescharacteristic
472C22×C8C2×#4111yescharacteristic
473C22×C8C2×#4111yescharacteristic
474C4⋊Q8—22no—
475C4⋊Q8—22no—
476C4⋊Q8—41no—
477C4⋊Q8—41no—
478#127—22no—
479#127—22no—
480#127—41no—
481#127—41no—
482#124—42no—
483#124—42no—
484#124—42no—
485#124—42no—
486#121—24no—
487#121—24no—
488#121—42no—
489#121—42no—
490#121—42no—
491#121—42no—
492#121—42no—
493#121—42no—
494C4×D4—24no—
495C4×D4—24no—
496C4×D4—24no—
497C4×D4—24no—
498C4×D4—24no—
499C4×D4—24no—
500C4×D4—42no—
501C4×D4—42no—
502C4×D4—42no—
503C4×D4—42no—
504C4×D4—42no—
505C4×D4—42no—
506C4×D4—42no—
507C4×D4—42no—
508C4×D4—42no—
509C4×D4—42no—
510C4×D4—42no—
511C4×D4—42no—
512C4×D4—42no—
513C4×D4—42no—
514C4×D4—42no—
515C4×D4—42no—
516C4×D4—42no—
517C4×D4—42no—
518C2×C4⋊C4—22no—
519C2×C4⋊C4—22no—
520C2×C4⋊C4—22no—
521C2×C4⋊C4—22no—
522C2×C4⋊C4—41no—
523C2×C4⋊C4—41no—
524C2×C4⋊C4—41no—
525C2×C4⋊C4—41no—
526C2×C22⋊C4—42no—
527C2×C22⋊C4—42no—
528C2×C22⋊C4—42no—
529C2×C22⋊C4—42no—
530C2×C22⋊C4—42no—
531C2×C22⋊C4—42no—
532C2×C22⋊C4—42no—
533C2×C22⋊C4—42no—
534C2×C42C4×D411yescharacteristic
535C2×C42C4×D411yescharacteristic
536C2×C42C4×D411yescharacteristic
537C2×C42AGL(1,ℤ/8)11yescharacteristic
538C2×C42AGL(1,ℤ/8)11yescharacteristic
539C2×C42AGL(1,ℤ/8)11yescharacteristic
540C2×C42AGL(1,ℤ/8)11yescharacteristic
541C2×C42AGL(1,ℤ/8)11yescharacteristic
542C2×C42AGL(1,ℤ/8)11yescharacteristic
543C2×C42C22×D411yescharacteristic
544C2×C42C22×D411yescharacteristic
545C2×C42C22×D411yescharacteristic
546D16—416no—
547M32—44no—
548C2×C16—28no—
549C2×C16—24no—
550C2×C16C23×C418yes—
551#107—22no—
552#107—22no—
553#107—22no—
554#107—22no—
555#107—22no—
556#107—22no—
557#107C23×C414yes—
558#107C23×C414yes—
559C4⋊C8—21no—
560C4⋊C8—22no—
561C4⋊C8—21no—
562C4⋊C8—21no—
563C4⋊C8—21no—
564C4⋊C8—22no—
565C4⋊C8—24no—
566C4⋊C8—24no—
567C4⋊C8—42no—
568C4⋊C8—42no—
569#102—24no—
570#102—24no—
571#102—24no—
572#102—24no—
573#102—24no—
574#102—24no—
575#102—24no—
576#102—24no—
577C22⋊C8—21no—
578C22⋊C8—21no—
579C22⋊C8—21no—
580C22⋊C8—21no—
581C22⋊C8—22no—
582C22⋊C8—22no—
583C22⋊C8—48no—
584C22⋊C8—48no—
585C22⋊C8—48no—
586C22⋊C8—48no—
587C22⋊C8—42no—
588C22⋊C8—42no—
589C22⋊C8—42no—
590C22⋊C8—42no—
591#97—42no—
592C4×C8—22no—
593C4×C8—22no—
594C4×C8—42no—
595C4×C8—42no—
596C4×C8—42no—
597C4×C8C4×D411yescharacteristic
598C4×C8C4×D411yescharacteristic
599C4×C8C4×D411yescharacteristic
600C4×C8C4×D411yescharacteristic
601C4×C8C4×D411yescharacteristic
602C4×C8C4×D411yescharacteristic
603C4×C8C23×C411yescharacteristic
604C4×C8C23×C411yescharacteristic
605C4×C8C23×C411yescharacteristic
606C4×C8C22×D412yes—
607C4×C8C22×D412yes—
608C4×C8C22×D412yes—
609C4×C8C22×D412yes—
610C4×C8C22×D411yescharacteristic
611C4×C8C22×D411yescharacteristic
612C4×C8C22×D411yescharacteristic
613C4×C8C2×#4111yescharacteristic
614C4×C8C2×#4111yescharacteristic
615C4×C8C2×#4111yescharacteristic
616C4×C8C2511yescharacteristic
617C24—42no—
618C24—42no—
619C24—42no—
620C24—42no—
621C24—84no—
622C24—162no—
623C24—162no—
624C24#44211yescharacteristic
625#41—88no—
626#41—164no—
627#41—164no—
628#41—164no—
629C2×Q8—42no—
630C2×Q8—42no—
631C2×Q8—162no—
632C2×D4—24no—
633C2×D4—24no—
634C2×D4—44no—
635C2×D4—44no—
636C2×D4—44no—
637C2×D4—44no—
638C2×D4—44no—
639C2×D4—44no—
640C2×D4—44no—
641C2×D4—44no—
642C2×D4—42no—
643C2×D4—42no—
644C2×D4—42no—
645C2×D4—42no—
646C2×D4—42no—
647C2×D4—42no—
648C2×D4—42no—
649C2×D4—42no—
650C2×D4—44no—
651C2×D4—44no—
652C2×D4—84no—
653C2×D4—84no—
654C2×D4—84no—
655C2×D4—162no—
656C2×D4—162no—
657C2×D4—164no—
658C22×C4—22no—
659C22×C4—22no—
660C22×C4—42no—
661C22×C4—42no—
662C22×C4—42no—
663C22×C4—42no—
664C22×C4—42no—
665C22×C4—42no—
666C22×C4—44no—
667C22×C4—44no—
668C22×C4—44no—
669C22×C4—44no—
670C22×C4—44no—
671C22×C4—44no—
672C22×C4—88no—
673C22×C4—164no—
674C22×C4—164no—
675C22×C4—164no—
676C22×C4—164no—
677C22×C4—164no—
678C22×C4—164no—
679C22×C4—162no—
680C22×C4#44211yescharacteristic
681C22×C4#44211yescharacteristic
682C22×C4#44211yescharacteristic
683C22×C4#44211yescharacteristic
684C22×C4#44211yescharacteristic
685C22×C4#44211yescharacteristic
686C22×C4#44211yescharacteristic
687C22×C4#44211yescharacteristic
688C22×C4#44211yescharacteristic
689C22×C4C2×C4×D411yescharacteristic
690C22×C4C2×C4×D411yescharacteristic
691C22×C4C2×C4×D411yescharacteristic
692C22×C4C2×AGL(1,ℤ/8)11yescharacteristic
693C22×C4C2×AGL(1,ℤ/8)11yescharacteristic
694C22×C4C2×AGL(1,ℤ/8)11yescharacteristic
695C22×C4C2×AGL(1,ℤ/8)11yescharacteristic
696C22×C4C2×AGL(1,ℤ/8)11yescharacteristic
697C22×C4C2×AGL(1,ℤ/8)11yescharacteristic
698D8—24no—
699D8—28no—
700D8—24no—
701D8—44no—
702D8—44no—
703D8—44no—
704D8—44no—
705D8—44no—
706D8—44no—
707M16—84no—
708M16—168no—
709M16—168no—
710M16—168no—
711C2×C8—22no—
712C2×C8—22no—
713C2×C8—22no—
714C2×C8—22no—
715C2×C8—22no—
716C2×C8—22no—
717C2×C8—22no—
718C2×C8—22no—
719C2×C8—22no—
720C2×C8—22no—
721C2×C8—22no—
722C2×C8—41no—
723C2×C8—41no—
724C2×C8—41no—
725C2×C8—41no—
726C2×C8—44no—
727C2×C8—44no—
728C2×C8—44no—
729C2×C8—44no—
730C2×C8—84no—
731C2×C8—168no—
732C2×C8C2×C4×D411yescharacteristic
733C2×C8C2×C4×D411yescharacteristic
734C2×C8C2×C4×D411yescharacteristic
735C2×C8C2×C4×D411yescharacteristic
736C2×C8C2×C4×D411yescharacteristic
737C2×C8C2×C4×D411yescharacteristic
738C2×C8#56814yes—
739C2×C8C24×C411yescharacteristic
740C2×C8C22×#4111yescharacteristic
741C4⋊C4—24no—
742C4⋊C4—24no—
743C4⋊C4—42no—
744C4⋊C4—42no—
745C4⋊C4—42no—
746C4⋊C4—42no—
747C4⋊C4—42no—
748C4⋊C4—42no—
749C22⋊C4—44no—
750C22⋊C4—44no—
751C22⋊C4—44no—
752C22⋊C4—44no—
753C22⋊C4—44no—
754C22⋊C4—44no—
755C22⋊C4—44no—
756C22⋊C4—44no—
757C42#44211yescharacteristic
758C42#44211yescharacteristic
759C42#44211yescharacteristic
760C42#44211yescharacteristic
761C42#44211yescharacteristic
762C42#44211yescharacteristic
763C42C2×C4×D411yescharacteristic
764C42C2×C4×D411yescharacteristic
765C42C2×C4×D411yescharacteristic
766C42C2×AGL(1,ℤ/8)11yescharacteristic
767C42C2×AGL(1,ℤ/8)11yescharacteristic
768C42C2×AGL(1,ℤ/8)11yescharacteristic
769C42C2×AGL(1,ℤ/8)11yescharacteristic
770C42C2×AGL(1,ℤ/8)11yescharacteristic
771C42C2×AGL(1,ℤ/8)11yescharacteristic
772C42C23×D411yescharacteristic
773C16—28no—
774C16—44no—
775C23—22no—
776C23—22no—
777C23—41no—
778C23—44no—
779C23—44no—
780C23—84no—
781C23—84no—
782C23—84no—
783C23—84no—
784C23—84no—
785C23—84no—
786C23—162no—
787C23—162no—
788C23—162no—
789C23—162no—
790C23—162no—
791C23—162no—
792C23—1616no—
793C23C2×#44211yescharacteristic
794C23C2×#44211yescharacteristic
795C23C2×#44211yescharacteristic
796Q8—84no—
797Q8—162no—
798D4—44no—
799D4—44no—
800D4—44no—
801D4—44no—
802D4—84no—
803D4—84no—
804D4—84no—
805D4—88no—
806D4—84no—
807D4—84no—
808D4—84no—
809D4—162no—
810D4—162no—
811D4—164no—
812C2×C4—22no—
813C2×C4—22no—
814C2×C4—22no—
815C2×C4—22no—
816C2×C4—22no—
817C2×C4—21no—
818C2×C4—21no—
819C2×C4—22no—
820C2×C4—22no—
821C2×C4—22no—
822C2×C4—21no—
823C2×C4—21no—
824C2×C4—41no—
825C2×C4—41no—
826C2×C4—41no—
827C2×C4—41no—
828C2×C4—41no—
829C2×C4—41no—
830C2×C4—41no—
831C2×C4—44no—
832C2×C4—44no—
833C2×C4—88no—
834C2×C4—88no—
835C2×C4—84no—
836C2×C4—88no—
837C2×C4—164no—
838C2×C4—164no—
839C2×C4—164no—
840C2×C4—162no—
841C2×C4—162no—
842C2×C4—162no—
843C2×C4#293012yes—
844C2×C4C2×#44211yescharacteristic
845C2×C4C2×#44211yescharacteristic
846C2×C4C2×#44211yescharacteristic
847C2×C4C2×#44211yescharacteristic
848C2×C4C2×#44211yescharacteristic
849C2×C4C2×#44211yescharacteristic
850C2×C4C2×#44211yescharacteristic
851C2×C4C2×#44211yescharacteristic
852C2×C4C2×#44211yescharacteristic
853C2×C4#295512yes—
854C2×C4C22×C4×D411yescharacteristic
855C2×C4C22×AGL(1,ℤ/8)11yescharacteristic
856C2×C4C22×AGL(1,ℤ/8)11yescharacteristic
857C8—21no—
858C8—21no—
859C8—21no—
860C8—21no—
861C8—21no—
862C8—21no—
863C8—42no—
864C8—42no—
865C8—42no—
866C8—42no—
867C8—84no—
868C8—84no—
869C8#293012yes—
870C8C2×#56812yes—
871C22—21no—
872C22—21no—
873C22—21no—
874C22—21no—
875C22—21no—
876C22—21no—
877C22—21no—
878C22—44no—
879C22—84no—
880C22—84no—
881C22—84no—
882C22—84no—
883C22—84no—
884C22—84no—
885C22—168no—
886C22—168no—
887C22—168no—
888C22—324no—
889C22#1793512yes—
890C22#3347112yes—
891C22C22×#44211yescharacteristic
892C4—21no—
893C4—21no—
894C4—21no—
895C4—21no—
896C4—21no—
897C4—21no—
898C4—21no—
899C4—21no—
900C4—21no—
901C4—84no—
902C4—84no—
903C4#1793512yes—
904C4#3347112yes—
905C4C2×#293011yescharacteristic
906C4C2×#295511yescharacteristic
907C2—22no—
908C2—22no—
909C2—41no—
910C2—164no—
911C2—164no—
912C2C2×#1793511yescharacteristic
913C2C2×#3347111yescharacteristic
914C2C2×#3347111yescharacteristic
subgroupG/H
center, socleC22C22×#442
commutatorC2×C8C24×C4
Frattini, cosocleC4×C8C25
prime radicalC2×#33669C2
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ C22×C42 ◁ C2×#1450 ◁ G
LECSG ▷ C4×C8 ▷ C2×C4 ▷ C2 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. #6344817C2semidirect
3. C2×#17895C2semidirect
4. #483934C2semidirect
5. #483921C2semidirect
6. #483843C2semidirect
7. #483813C2semidirect
8. #483420C2semidirect
9. #481315C2semidirect
10. #481279C2semidirect
11. #479969C2semidirect
28. #17970C22semidirect
29. #17962C22semidirect
37. #17895C22semidirect
38. #17895C22semidirect
39. C2×#1594C22semidirect
42. #17854C22semidirect
48. #12089C22semidirect
49. #12078C22semidirect
50. #12031C22semidirect
51. #12030C22semidirect
52. #11999C22semidirect
53. #11667C22semidirect
54. #11663C22semidirect
55. #11654C22semidirect
56. #11652C22semidirect
58. #11599C22semidirect
59. #11416C22semidirect
60. #11415C22semidirect
61. #11406C22semidirect
62. #11405C22semidirect
149. #1594C23semidirect
157. #1580C23semidirect
188. #1368C23semidirect
190. #1333C23semidirect
191. #1313C23semidirect
192. #1313C23semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#336692
#63448172
C2×#178952
#4839342
#4839212
#4838432
#4838132
#4834202
#4813152
#4812792
#4799692